Methods and systems are provided for adjusting a steering torque threshold for automatically stopping and starting a vehicle engine. In one example, a method may include, while the engine is running, determining a first steering torque threshold for inhibiting stop-start of the engine based on a steering wheel angle, and, while the engine is auto-stopped, determining a second steering torque threshold for inhibiting the stop-start based on the steering wheel angle and whether a static stop-start event is present or a rolling stop-start event is present. In this way, a non-linear hysteresis is provided for automatically stopping and starting the engine.